## Current Electricity

## Electric Current and Ohm’s Law Multiple Choice Question And Answers

**Question 1. Consider a current-carrying wire (current 7) in the shape of a circle. Note that as the current progresses along the wire, the direction of current density \(\vec{j}\) changes in an exact manner, while the current I remains unaffected. The agent that is essentially responsible for**

- Source of emf
- The electric field produced by charges accumulated on the surface of the wire
- The charges just behind a given segment of wire push them just the right way by repulsion
- The charges ahead

**Answer:** 2. Electric field produced by charges accumulated on the surface of the wire

**Question 2. Two batteries of emf e _{1} and e_{2}(e_{2} > e_{1}) and internal resistances r_{1} and r_{2} respectively are connected in parallel**

**The equivalent of the two cells is eeq.**

- e
_{1}< e_{eq}< e_{2} - e
_{eq}< e_{1} - e
_{eq}= e_{1}+ e_{2} - e
_{eq}is independent of and r_{2}

**Answer:** 1. el e_1 \text {, let } e_2=e_1+\Delta e[/latex]

∴ \(\frac{e_{\mathrm{eq}}}{r_{\mathrm{eq}}}=\frac{e_1}{r_1}+\frac{e_1+\Delta e}{r_2}=e_1\left(\frac{1}{r_1}+\frac{1}{r_2}\right)+\frac{\Delta e}{r_2}\)

\(\frac{e_1}{r_{\mathrm{eq}}}+\frac{\Delta e}{r_2}\)∴ e_{eq} > e_{1}

Again,

∴ \(\frac{e_{\mathrm{eq}}}{r_{\mathrm{eq}}}=\frac{e_2}{r_{\mathrm{eq}}}-\frac{\Delta e}{r_1} \text { or, } e_{\mathrm{eq}}<e_2\)

e_{1} < e_{eq} < e_{2}

**Question 3. Temperature dependence of resistivity p(T) of semiconductors, insulators, and metals is significantly based on which of the following factors?**

- The number of charge carriers can change with temperature T
- The time interval between two successive collisions can depend on the T
- The length of the material can be a function of T
- The mass of carriers is a function of the T

**Answer:**

1. The number of charge carriers can change with temperature T

2. The time interval between two successive collisions can depend on the T

**Question 4. The current in a conductor varies with time t as I = 2t+ 3t², where I is in ampere and t in second. Electric charge flowing through a section of the conductor during t = 2s to f = 3s is**

- 10C
- 24 C
- 33 C
- 44 C

**Answer:** 2. 24 C

**Question 5. Fmf of a lead-acid accumulator during its prolonged discharging is**

- 1.08 V
- 1.5 V
- 2.0 V
- 2.2 V

**Answer:** 3. 2.0 V

**Question 6. What energy transformation occurs during the discharging of an accumulator?**

- Electrical energy to chemical energy
- Chemical energy to electrical energy
- Electrical energy to mechanical energy
- Mechanical energy to electrical energy

**Answer:** 2. Chemical energy to electrical energy

**Question 7. What is the nature of energy conversion during the charging of a secondary cell?**

- Electrical energy to chemical energy
- Chemical energy to electrical energy
- Electrical energy to mechanical energy
- Mechanical energy to electrical energy

**Answer:** 1. Electrical energy to chemical energy

**Question 8. Which of the following graphs represents the variation of current (7) through a metallic conductor with its terminal potential difference (V)?**

**Answer:** 1.

**Question 6. The dimension of resistance is**

- \(\mathrm{ML}^2 \mathrm{~T}^{-3} \mathrm{I}^{-1}\)
- \(\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{I}^{-1}\)
- \(\mathrm{ML}^2 \mathrm{~T}^{-3} \mathrm{I}^{-2}\)
- \(\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{I}^{-2}\)

**Answer:** 3. \(\mathrm{ML}^2 \mathrm{~T}^{-3} \mathrm{I}^{-2}\)

**Question 9. The resistivity of copper is 1.76 x 10 ^{-6} Ω.cm. What will be the resistance between two opposite faces of a copper cube of side 1 m?**

- 1.76 x 10
^{-4}Ω - 1.76 x 10
^{-6}Ω - 1.76 x 10
^{-8}Ω - 1.76 x 10
^{-12}Ω

**Answer:** 3. 1.76 x 10^{-8}Ω

**Question 10. A block has dimensions 1 cm, 2 cm, and 3 cm. The ratio of the maximum and minimum distance between any two points of opposite faces of this block is**

- 1:6
- 1:9
- 9:1
- 18:1

**Answer:** 3. 9:1

**Question 11. A conductor with a rectangular cross-section has dimensions (a x 2a x 4a). Resistance across AB is R _{1}, across CD is R_{2}, and across EF is R_{3}. Then**

- R
_{1}= R_{2}= R_{3} - R
_{1}> R_{2}> R_{3} - R
_{2}> R_{3}> R_{1} - R
_{1}> R_{3}> R_{2}

**Answer:** 4. R_{1} > R_{3} > R_{2}

**Question 12. A wire of resistance 4 Ω is bent through 180° at its midpoint and the two halves are twisted together. Then the resistance is**

- 1Ω
- 2Ω
- 5Ω
- 8Ω

**Answer:** 1. 1 Ω

**Question 13. The temperature coefficient of resistance of a metal is 0.004°C ^{-1}. If a wire of this metal has resistance 1 CL at 0°C then what will be the value of that resistance at 100°C?**

- 0.6Ω
- 0.96Ω
- 1.04Ω
- 1.4Ω

**Answer:** 4. 1.4 Ω

**Question 14. A carbon resistor has a resistance of 10 ^{6} x 1. The color of its third band is**

- Yellow
- Green
- Blue
- Violet

**Answer:** 2. Green

**Question 15. The resistance of a wire is 5 Ω at 50°C and 6 Ω at 100°C. The resistance of the wire at 0°C will be**

- 1Ω
- 2Ω
- 3Ω
- 4Ω

**Answer:** 4. 4Ω

**Question 16. If three resistances, connected in series, are related as R _{1}>R_{2}> R_{3} then what is the relation between the currents flowing through them?**

- I
_{1}= I_{2}= I_{3} - I
_{1}> I_{2}> I_{3} - I
_{1}< I_{2}< I_{3} - I
_{1}> I_{3}> I_{2}

**Answer:** 1. I_{1} = I_{2} = I_{3}

**Question 17. If three resistances are connected in parallel and the relation between them is R _{1 }> R_{2 }> R_{3}, then the relation between the currents flowing through them is**

- I
_{1}= I_{2}= I_{3} - I
_{1}> I_{2}> I_{3} - I
_{1}< I_{2}< I_{3} - I
_{3}< I_{1}< I_{2}

**Answer:** 3. I_{1} < I_{2} < I_{3}

**Question 18. Two resistances of 6Ω and 3Ω are connected in parallel and this combination is connected to a battery of emf 2 V. What will be the current flowing through the 6Ω resistance?**

- \(\frac{1}{3}\)A
- \(\frac{2}{3}\)A
- 1A
- 2A

**Answer:** 1. \(\frac{1}{3}\)A

**Question 19. A series combination of three resistances 1Ω, 2Ω, and 3Ω is connected with a cell of emf 1.5 V and negligible internal resistance. What is the terminal potential difference across the third resistance?**

- \(\frac{1}{4}\)V
- \(\frac{1}{2}\)V
- \(\frac{3}{4}\)V
- 1V

**Answer:** 3. \(\frac{3}{4}\)V

**Question 20. A uniform metal wire of resistance R is stretched to twice its length. Now this wire is halved, and the two halves are connected in parallel. The equivalent resistance is**

- \(\frac{R}{2}\)
- R
- 2R
- 4R

**Answer:** 2. R

**Question 21. Which of the following is correct?**

- 0.50A current flows in 3Ω
- 0.25A current flows in 3Ω
- 0.50A current flows in 4Ω
- 0.25A current flows in 4Ω

**Answer:** 4. 0.25A current flows in 4Ω

**Question 22. The equivalent resistance between points A and B is**

- 3Ω
- 4Ω
- 6Ω
- 11Ω

**Answer:** 2. 4Ω

**Question 23. A set of n identical resistors, each of resistance R ohm when connected in series, has effective resistance X ohm, and when connected in parallel the effective resistance is Y ohm. The relation between R, X, and Y is given by**

- \(R=\sqrt{X Y}\)
- \(R=Y \sqrt{X}\)
- \(R=X \sqrt{Y}\)
- \(\sqrt{R}=X Y\)

**Answer:** 1. \(R=\sqrt{X Y}\)

**Question 24. A uniform wire of resistance 36Ω is bent in the form of a circle. The equivalent resistance across the points A and B is**

- 36Ω
- 18Ω
- 9Ω
- 2.75Ω

**Answer:** 4. 2.75Ω

**Question 25. What is the equivalent resistance across points A and B?**

- 8Ω
- 12Ω
- 16Ω
- 32Ω

**Answer:** 1. 8Ω

**Question 26. Six equal resistances are connected between points P, Q, and R. Then, the equivalent resistance will be maximum between**

- P and Q
- Q and R
- P and R
- Any two points

**Answer:** 1. P and Q

**Question 27. The resistance across A and B in the below will**

- 3B
- R
- \(\frac{R}{3}\)
- None of the above

**Answer:** 3. R

**Question 28. A ring is made of a wire having a resistance RQ = 12Ω. Find the points A and B at which a current-carrying conductor should be connected so that the resistance R of the subcircuit between these points is equal to \(\frac{8}{3}\)Ω**

- \(\frac{l_1}{l_2}=\frac{5}{8}\)
- \(\frac{l_1}{l_2}=\frac{1}{3}\)
- \(\frac{l_1}{l_2}=\frac{3}{8}\)
- \(\frac{l_1}{l_2}=\frac{1}{2}\)

**Answer:** 4. \(\frac{l_1}{l_2}=\frac{1}{2}\)

**Question 29. A cell of emf E and internal resistance r is connected to an external resistance R. The variation of potential drop V across the resistance R as a function of R is shown by the curve marked as**

- 4
- 1
- 2
- 3

**Answer:** 3. 2

**Question 30. A current of 0.1 A flows through a 12Ω resistance when it is connected to a cell of emf 1.5 V. The internal resistance of the cell is**

- 1Ω
- 3Ω
- 5Ω
- 15Ω

**Answer:** 2. 3Ω

**Question 31. When a resistance of 12Ω is connected with a cell of emf 1.5 V, 0.1 A current flows through the resistance. The internal resistance of the cell is**

- 1Ω
- 3Ω
- 5Ω
- 1.5Ω

**Answer:** 2. 3Ω

**Question 32. A shunt resistance 1Ω is connected with a galvanometer of resistance 100Ω. What part of the main current will flow through the galvanometer?**

- \(\frac{1}{99}\)
- \(\frac{1}{100}\)
- \(\frac{1}{101}\)
- \(\frac{1}{98}\)

**Answer:** 3. \(\frac{1}{101}\)

**Question 33. A galvanometer of resistance R is connected to an electric circuit. The main current in the circuit is k times the maximum current that the galvanometer can withstand. The maximum value of the shunt resistance that should be used across the galvanometer is**

- kR
- (k-1)R
- \(\frac{R}{k}\)
- \(\frac{R}{k-1}\)

**Answer:** 4. \(\frac{R}{k-1}\)

**Question 34. Three voltmeters, all having different resistances, are joined. When some potential differences are applied across P and Q, their readings are V _{1}, V_{2}, and V_{3} respectively. Then**

- V
_{1}= V_{2} - V
_{1}≠ V_{2}+ V_{3} - V
_{1}+ V_{2 }= V_{3} - V
_{1}+ V_{2}> V_{3}

**Answer:** 3. V_{1} + V_{2} = V_{3}

**Question 35. Two electric cells each of emf 1.5 V and internal resistance 2Ω are connected in parallel and this combination of cells is connected with an external resistance of 2Ω. What will be the current in the external circuit?**

- \(\frac{1}{4}\)A
- \(\frac{1}{3}\)A
- \(\frac{1}{2}\)A
- 1A

**Answer:** 3. \(\frac{1}{2}\)A

**Question 36. n identical cells, each of emf e and internal resistance r, are first connected in series and then in parallel. What will be the ratio of the emf and of the internal resistances of these two cell combinations?**

- n, n
- n,n²
- n²,n
- \(\frac{1}{n}\) , n

**Answer:** 2. n,n²

**Question 37. Two cells each of emf e but of internal resistance r _{1} and r_{2} are connected in series through an external resistance R. If the potential difference across the first cell is zero while current flows, the value of R in terms of r_{1} and r_{2} is**

- R = r
_{1}+ r_{2} - R = r
_{1}– r_{2} - R = \(\frac{1}{2}\)(r
_{1}+ r_{2}) - R = \(\frac{1}{2}\)(r
_{1}– r_{2})

**Answer:** 2. R = r_{1} – r_{2}

**Question 38. A galvanometer connected with an unknown resistor and two identical cells in series each of emf 2 V, shows a current of 1 A. If the cells are connected in parallel, it shows 0.8 A. Then the internal resistance of the cell is**

- 1Ω
- 2.8Ω
- 0.7Ω
- 1.4Ω

**Answer:** 1. 1Ω

**Question 39. In a metallic conductor, the number of free electrons per unit volume is n and the drift velocity of those electrons is vd. Then**

- \(v_d \propto n\)
- \(v_d \propto \frac{1}{n}\)
- \(v_d \propto n^2\)
- \(v_d \propto \frac{1}{n^2}\)

**Answer:** 2. \(v_d \propto n^2\)

**Question 40. When a current of 1 A flows through a copper wire of cross-sectional area 1 mm², the drift velocity of free electrons becomes v. What will be the drift velocity of free electrons when the same current flows through a copper wire of cross-sectional area 2 mm²?**

- \(\frac{v}{2}\)
- v
- 2v
- 4v

**Answer:** 1. \(\frac{v}{2}\)